Carlos Tschudi Simpson (born 30 June 1962) is an American mathematician, specializing in algebraic geometry.
Simpson received his
Ph.D. in 1987 from
Harvard University
Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of high ...
, where he was supervised by
Wilfried Schmid; his thesis was titled ''Systems of Hodge Bundles and Uniformization''. He became a professor at the University of Toulouse III (
Paul Sabatier University) and then at the
University of Nice. He is research director of the
Centre national de la recherche scientifique.
He works on moduli spaces of
vector bundle
In mathematics, a vector bundle is a topological construction that makes precise the idea of a family of vector spaces parameterized by another space X (for example X could be a topological space, a manifold, or an algebraic variety): to ev ...
s, higher non-abelian
de Rham cohomology
In mathematics, de Rham cohomology (named after Georges de Rham) is a tool belonging both to algebraic topology and to differential topology, capable of expressing basic topological information about smooth manifolds in a form particularly adap ...
(
Hodge theory), the theory of
higher categories and computer verification of mathematical proofs (''e.g.'' verification of proofs within
Zermelo–Fraenkel set theory using
Coq). In his Ph.D. dissertation, Simpson studied the notion of system of
Hodge bundle In mathematics, the Hodge bundle, named after W. V. D. Hodge, appears in the study of families of curves, where it provides an invariant in the moduli theory of algebraic curves. Furthermore, it has applications to the theory of modular forms on ...
s, which can be seen as a special case of the higher dimensional generalization of
Higgs bundle
In mathematics, a Higgs bundle is a pair (E,\varphi) consisting of a holomorphic vector bundle ''E'' and a Higgs field \varphi, a holomorphic 1-form taking values in the bundle of endomorphisms of ''E'' such that \varphi \wedge \varphi=0. Such pa ...
s introduced earlier by
Nigel Hitchin. The
Simpson correspondence
In algebraic geometry and differential geometry, the nonabelian Hodge correspondence or Corlette–Simpson correspondence (named after Kevin Corlette and Carlos Simpson) is a correspondence between Higgs bundles and representations of the fundamen ...
(or the Corlette-Simpson correspondence, named after
Kevin Corlette
Kevin () is the anglicized form of the Irish masculine given name (; mga, Caoimhghín ; sga, Cóemgein ; Latinized as ). It is composed of "dear; noble"; Old Irish and ("birth"; Old Irish ).
The variant '' Kevan'' is anglicized from , a ...
and Simpson) is a correspondence between Higgs bundles and representations of the
fundamental group of a smooth, complex
algebraic curve.
The Deligne–Simpson Problem, an algebraic problem associated with
monodromy matrices, is named after Carlos Simpson and
Pierre Deligne.
Simpson was an Invited Speaker with talk ''Nonabelian Hodge theory'' at the
International Congress of Mathematicians in 1990 at
Kyoto
Kyoto (; Japanese: , ''Kyōto'' ), officially , is the capital city of Kyoto Prefecture in Japan. Located in the Kansai region on the island of Honshu, Kyoto forms a part of the Keihanshin metropolitan area along with Osaka and Kobe. , the ...
. In 2015 he received the
Sophie Germain Prize The Sophie Germain Prize (in French: ''Prix Sophie Germain'') is an annual mathematics prize from the French Academy of Sciences conferred since the year 2003. It is named after the French mathematician Sophie Germain, and comes with a prize of € ...
.
Selected publications
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References
External links
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{{DEFAULTSORT:Simpson, Carlos
1962 births
Living people
20th-century American mathematicians
21st-century American mathematicians
Harvard University alumni
Academic staff of the University of Toulouse
Academic staff of Côte d'Azur University
Algebraic geometers
Topologists